F(x)=-x^2-9x-15

Solution for F(x)=-x^2-9x-15 equation:

(F)=-F^2-9F-15

We move all terms to the left:

(F)-(-F^2-9F-15)=0

We get rid of parentheses

F^2+9F+F+15=0

We add all the numbers together, and all the variables

F^2+10F+15=0

a = 1; b = 10; c = +15;
Δ = b2-4ac
Δ = 102-4·1·15
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{10}}{2*1}=\frac{-10-2\sqrt{10}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{10}}{2*1}=\frac{-10+2\sqrt{10}}{2}
$